A new approach to finite element modelling of cyclic thermomechanical stress-strain responses

Modem finite element based structural analyses of thermomechanically loaded structures require accurate simulations with low computational times. However, increasing the complexity of material models capable of modelling cyclic phenomena of engineering materials usually also increases the computational time. Here we present the implementation of the Prandtl operator approach into a finite element solver as a new material model for the study of the stress-strain response of solids subjected to thermomechanical loading. The main advantage of this model is its high computational speed, due mainly to the implicit consideration of the Masing and memory rules by variable temperatures, either during a single load cycle or during a complex thermomechanical load history. The model enables temperature-dependent elastoplastic stress-strain modelling using the von Mises yield function, associated flow rule and multilinear kinematic hardening. The commonly used elastic predictor-plastic corrector procedure now contains an improvement in the calculation of the equivalent plastic strain increment. This includes modelling of the true stress by the time-efficient temperature-dependent spring-slider model. The second advantage of the approach is a reduced number of material parameters per temperature required by the Ramberg-Osgood-type description of the cyclic curve. These material parameters can be obtained from either uniaxial strain controlled low cycle fatigue tests or uniaxial incremental step tests. The model has been validated on several load cases of both a thermomechanically loaded single finite element under tension-compression and shear loads, and a cantilever beam subjected to bending loads. Comparisons with reference material models show almost identical behaviour of the new and the Besseling model, but with the advantage of having up to 35 percent shorter computation times.